School Doesn't Have to Suck When You Teach Your Own Kids

One of the problems my son ran into when he still attended a brick-and-mortar school is the current mania for turning every damned arithmetic problem into the equivalent of a New York cabbie taking a rube tourist to Rockefeller Center via Staten Island. Why go the direct route when you can run up the meter?

Fortunately, my son is now homeschooled—or, technically, attends a private online school. He uses online lessons and offline texts and workbooks to learn, coached by his mother and me. The lessons are means to an end; he takes them as needed, and can take as much or little time as necessary, until he demonstrates his mastery of a topic in a unit assessment test. Then he moves on. Find your vocabulary set a breeze? Then skip the review lessons. Stumped by long division? Then spend a few hours working it out.

And when the approach recommended by the book comes from education-establishment bizarro land, we can explain (not ask permission) in a conversation with his homeroom teacher (really, an advisor/contact at the school) that we won't be taking the scenic route across a mathematical Verrazano-Narrows Bridge. Instead, my wife taught Anthony basic long division as she learned the subject. He has my mind for math which is, admittedly, missing a few circuits, so that was challenging enough. So she spread the lesson over two days. And she had him work at it repeatedly.

And he passed his unit assessment with 100 percent. Even better, he said he liked math. Last year he cried over his homework.

Editor's Note: We invite comments and request that they be civil and on-topic. We do not moderate or assume any responsibility for comments, which are owned by the readers who post them. Comments do not represent the views of Reason.com or Reason Foundation. We reserve the right to delete any comment for any reason at any time. Report abuses.

experts disagree over whether it’s Common Core’s fault or whether the education establishment is blowing the teaching of math without assistance from the controversial new standards.

It’s definitely the latter. No ammount of centralized control over the curriculum can make up for shitty teachers. Although, it’s disheartening to see the shittily implemented curriculum that is common core effectively kneecap my daughter’s teachers.

It’s not just the implementation. I had a long discussion last week with my 4th grader’s math teacher. The TESTS* they will be testing them with are driving a great deal of the problem. He’s learning 4 different ways to solve basic 2 digit multiplication problems and on the test they will be required to solve problems IN THOSE SPECIFIC WAYS. So if he understand 22*45 the normal way, and gets the answer right, but doesn’t draw a box model to solve it, he won’t get full credit. So the test is forcing the children to master 4 different methods. The idea that they are exposed to different methods so they can pick what works with their learning style is a great one. Testing them on all of the methods themselves is beyond stupid.

Of course, I’m convinced from reading the union propaganda my mom got in her days as a teachers’ aide that the education system is deliberately using jargon to try to keep us non-professionals from understanding what they’re doing.

Socialization isn’t a huge issue, but, given modern sensibilities, one thing we have seen with our daughter is a greater attachment to us than is common with most kids. That’s a little tricky, but I’d rather we be disproportionately influential than some teacher or peer, both of which are largely idiots from our perspective.

That’s where the bottom solution comes into play. I admit it’s totally confusing but here’s what it’s saying:

If you want to subtract 12 from 32, there’s a better way to think about it. Forget the algorithm. Instead, count up from 12 to an “easier” number like 15. (You’ve gone up 3.) Then, go up to 20. (You’ve gone up another 5.) Then jump to 30. (Another 10). Then, finally, to 32. (Another 2.)

I know. That’s still ridiculous. Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill. How much change should the barista give you back? (Assume for a second the register is broken.)

Uh.. Wat? the ones place matches. Its actually just 3-1 in the tens place. Also, you should go DOWN from 32 by 12. I don’t understand. The algorithm is simple. It takes, like 5 minutes to explain and then a couple hours of practice.

She thinks that some vague guesstimate approximation of mental math procedures as the paper process for math is better than the classic algorithm which can be applied to numbers of arbitrary size and is essential as a building block in of itself. She just hasn’t been called a dumbass nearly enough.

While the ‘new way’ seeks to emulate the mental math process, that process is A: sloppy, and B: developed internally after understanding the longhand method. The longhand methods are scalable to any size number. The mental math methods start to break down after a handful of orders of complexity. It’s the same way that sight words sabotage a beginning reader, because it looks like they’re learning, but then you overload the rote memory capacity and they are no longer able to expand their vocabulary.

Sight words (the common core method for reading) are like chinese characters. There is a great deal of lament in China over how few characters most people who have a chinese language as their native tongue can read. It’s all about building blocks – something you get with alphabets and arithmatic, but not with heiroglyphs and guesstimates

The longhand methods are scalable to any size number. The mental math methods start to break down after a handful of orders of complexity.

This strikes me as precisely the problem. I mean, maybe I’m a little cynical, but I can’t help but wonder how that technique winds up translating when you start looking at negative numbers or more complex mathematical processes.

“Well, consider this: Suppose you buy coffee and it costs $4.30 but all you have is a $20 bill.”

I know what she’s trying to explain, but she’s doing a poor job of it. She’s arguing for using shortcuts, which is a good idea, but her shortcuts as she explains them take longer than the traditional route.

No cashier is taught to count back change because all they have to do is enter the amount given to them and the change is calculated for them.

I love getting the A-student-in-non-advanced-courses cashier instead of the typical nimrod because their intellectual superiority is burst.

When I am given a price by a cashier of $6.37 and I hand them $21.52 the cashier more often than not tries to argue with me. I refuse to engage in conversation and refuse to take back the one dollar bill they try to hand me before entering into the register the amount I gave them. Then they look at me like I am from another planet when they actually type in $21.52 as the payment and see the magic change amount.

The typical moron cashier just enters the amount I gave them and gets puzzled at having to make 15 cents change with no dimes in the drawer.

Of course, the goddamned idiot teacher never would have thought of giving more than $20 to the cashier and gets stuck with a pile of overused ones and more dirty coins.

What they’re trying to teach is the way I do mental arithmetic – estimate and correct. It’s just doing arithmetic starting from the most significant digit rather than the least significant digit. It’s an OK way to do it, especially if you don’t have scratch paper.

It’s retarded to tell kids that they’re only allowed to use one algorithm to solve a problem. The answer is what matters, not the method. But more importantly…write a letter to Jack explaining why he sucks at math? Jesus Christ. That is not math.

The biggest thing I recall about High School chemistry is that another student complained that all I was doing was drawing in my notebook. The instructor saw that I was sketching isomers out of boredom and promptly ignored the complaints.

We didn’t do that. During the unit on polymerization, we did make silly putty (it came out white because we didn’t add pink dye), and we made brass pennies by electroplating them in zinc and heating them. (newer pennies have too little copper for that process)

I can’t say I had good english teachers at high school or college levels. They were the most bullshitty of the core subjects. The science and math teachers had some examples of good instructors, but they never broke more than a fraction of the faculty.

I found, for the most part (there were a few exceptions) that college instructors were far better than high school. The latter knew and enjoyed their fields, the former were usually pretty clueless about the subject and not particularly interested in learning it better.

I am very lucky. I was in a program for the gifted and the good teachers all wanted to be teaching us, so we got some really good ones. Some still sucked, and there was still a TON of deadtime in the curriculum.

Eh. I think you start with the precise algorithm for trivial cases and work outwards. Estimation is a valuable and extremely useful skill, but six year olds can be painfully literal. They don’t really have enough experiences to draw good generalizations (in general). So its good to expose them to that. But after they learn how to proceed to the exact solution by starting at the least significant digit and proceeding to the most.

I agree that they should start with the standard addition algorithm, but if a smart kid figures out some other way and it works for him, that should be cool. But obviously a government school is not going to be able to pull this off competently.

I always had problems in school with arithmetic because I don’t like rote memorization and multiplication tables bored the shit.out of.me. over the years I have developed any number.of.interesting techniques including factoring numbers that appear difficult to multiply in.my head and then solving the.simpler resulting problems. But I would never want to generalize something that works for me like that and try to standardize it. And I am an engineer.

Ain’t that bad? Well sir, there’s nothing on Earth like a genuine, bona-fide, electrified, six-car Common Core! It’s the only way to beat those inscrutable chinamen! Do you want to beat those inscrutable chinamen, or are you some kind of racist?

Instead, my wife taught Anthony basic long division as she learned the subject.

JD, I had the exact same experience with my son, a 4th grader. He is being taught how to do division in a way that takes a roundabout approach. When I try to explain to him the traditional algorithm, he gets frustrated and angry. When my wife spoke with his teacher about the problems my son was having, she started to tutor him earlier before bell ring on how to do long division the same way that I was teaching him. That alone was evidence of the utter failure of the new math approach she was teaching yet I am sure she is still inflicting it on other kids.

I just spoke with a co-worker and told me that her son is going through the same problem. She is also seeing the same reaction from his son at her attempts at explaining long division to him.

This tells me one thing: that there’s a concerted effort by school boards across the country to undermine the confidence of children on their parents’ abilities and knowledge, by turning a simple subject into something esoteric and thus privy to a few Experten. Who else, if not the unionized tax-consumers we call (with a sick sense of humor) “teachers”?

I can understand the approach of breaking arithmetic problems down into simpler problems with easy solutions–that is a microcosm of general problem solving. When I have to do a multiplication or division of large numbers in my head without benefit of paper or calculator, I often factor the numbers into easier multiplication problems and then add the results.

But doing this.for problems which should be.solvable.with either memorizAtion of multiplication tables or really.simple addition/subtraction principles is foolish, wasteful of.time, and confusing to students.

My issue is using it too soon. When basic arithmatic is first being introduced, you want the most stable, scalable, understandable building blocks you can get. After mastery of the process and the rote of the low digit arrays (ie 7×8=56, etc), moving on to shorthand and mental tricks is a good idea, as the longhand methods will serve as a backstop when the shorthand ones fail, or are unsuitable.

The one is about teaching people tricks to calculate quickly in their head, the other is about really teaching students the quickest way to figure a problem out on paper. What’s happened is someone has confused the former with the latter.

Does anyone remember a program called Individually Prescribed Instruction (IPI)? We used it in a (Quaker) grade school in the 70s.

You (and you alone) would take a “Pre-test” on a math subject. The test would determine if you already had mastery of the subject. If you failed a part or all of the test, you would work through a “skills” section to teach you the subject. After working thru the skills you’d take a “post-test” to demonstrate mastery of the concept.

Everyone worked at their own speed on their own material. We had third graders working on pre-algebra.

I feel for you. That must have been awful. All that inequality, just heartbreaking. Have you heard about Common Core? It solves all of those problems! Everyone working at the same pace in a gloriously synchronized environment! No messy individuality, no complications. Or else.

By the time I was in school, that approach was regarded as “discriminatory” and everyone was forced to cover the same material at the same pace. I had standing “do not answer questions posed in-class” orders pretty much eveyr year so that the teacher could throw them to the kids who didn’t understand the subject matter. I could have benefited from an IPI because instead I ended up being apathetic and not doing much of anything.

I knew 5th grade math before 1st grade. A 5th grader who hated math taught it to me (older sister) as sadistic entertainment. She had to get through the first 4 years of math first so it took a couple weeks.

It’s fairly evident that public school is for the 80% of society that we’d be better off without.

I do. I used it in 5th grade when I was assigned to the Mentally Gifted Minors program. It was marvelous and it totally ruined all future school for me for the rest of my public schooling. During that year, I took to it like a fish to water. I had finished Algebra I and was beginning trig by the end of the year. The school then stopped using that curricula and went back to the state recommended material. The teachers all claimed it was because they didn’t have enough money to continue the program because of Prop 13. From Trigonometry, I was back to fractions and long division. The boredom was almost unbearable; it would be another five years before I could continue where I left off. And yes I really like math, despite the public school’s best attempts to make me hate it.

The biggest problem with education is that memorization gets such a bad rap. Why does being able to instantly recall that 9 times 6 is 54 get frowned upon but coming up with some convoluted example to prove the same thing get taught over and over? Don’t bother memorizing the math fact. Change the 9 to 10, multiply by 6 to get 60, then subtract 6 off. To subtract 6 from 60, change the 6 to 10 – 4 so subtract 10 from 60 to get 50 then add 4 to get 54.

The punch line, of course, is that math is all memorization at some level.

If you don’t remember (because you memorized it) how do algebra, you’re not going to be able to do algebra. You have to memorize how the formulas go together and how they work, what all the symbols mean, and all that. Eventually, as you absorb the underlying logic, the memorization fades into your understanding.

But teaching any kind of math without understanding that it requires shitloads of memorization is like teaching Russian without realizing that it requires memorizing the Cyrillic alphabet, a whole bunch of words, and a whole bunch of grammar rules.

Just because they eventually become reflexive when you are fluent, doesn’t mean you didn’t have to memorize them to begin with.

Jerry Pournelle was a literal rocket scientist. I remember him describing mastering mathematics as learning the algorithm and then applying it to as many problems as necessary until you could execute it flawlessly. Hopefully, as you did this you acquired a sense of how different parameters affected whatever system was being modeled if you were doing engineering calculations. That has been my experience. Mastery of the algorithm often helps jumpstart conceptual synthesis. (“Oh, look at the 9s column in the multiplication table, they all add up to 9 or 18, that’s a good way to know if I’ve done it right. Also the tens column increments one and the ones column decrements one between rows 1 and 10”)

Quit trying. I started off the curriculum route with my kids, but quickly learned that unschooling actually works. Once the younglings reacquire their thirst for learning (if they’ve spent time in public school they might actually hate learning), you merely have to aim them at the appropriate books. Eventually they will be giving you lists of the appropriate books for you to beg borrow or steal for them.

I would feign illness on a school day. Mom would let me watch TV and I would eventually stop on the PBS station started by the City Colleges because the number of people trying to avoid the Viet Nam draft was so large they couldn’t accommodate them all in classrooms. Beat watching idiotic soap operas and game shows that required no intellect.

Note that the education establishment today considers TV College an abject failure.